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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Tests for Parallelograms

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Exercise 47 Page 503

Write an equation using given information.

x=4

Practice makes perfect

Let's begin with recalling that in a parallelogram diagonals bisect each other. Therefore, the distance between the point of intersection and vertex D is also 3x.

From the picture we can see that BD=6x. Since we know that AC is 40 and BD=35AC, we can write an equation to solve for x.

BD=6x

BD= 3/5AC

3/5AC=6x

AC= 40

3/5( 40)=6x

▼

Solve for x

MoveRightFacToNum

a/c* b = a* b/c

120/5=6x

a/b=.a /5./.b /5.

24/1=6x

a/1=a

24=6x

.LHS /6.=.RHS /6.

24/6=x

Calculate quotient

4=x

Rearrange equation

x=4

The quadrilateral ABCD is a parallelogram when x=4.

Subchapter links

Exercises p.499-503